Wave transmission network utilizing impedance inversion



May 25, 1954 J BANGERT 2,679,633

WAVE TRANSMISSION NETWORK UTILIZING IMPEDANCE INVERSION Filed 0012. 22. 1952 250 FIG. 4 F2 3200 k 3 g 150 8 100 E g 50 2 4 k s a FREQ uE/vcr- KC FIG. 5 H6. 6

& o FREQUENCY v '5 FREQUENCY FIG. 2 F/G.3 FIG. 7 FIG. 8

/4 14 44 /Z4 l l c 56, T 1 /C/ R /L3 15 FIG. /0 FIG.

uwg/vrox? J. 2 RANGE/PT BY A TTORNEV Patented May 25, 1954 UNITED STATES OFFICE WAVE TRANSMISSION NETWQEK UTIU Z'WG IMPEDANCE INVERSION Application October 22, 1952; serial N 3165298 (01. sea-80) 30 Claims.

This invention relates to wave: transmission net'- works and more particularly to those utilizing; a transistor to elfect an impedanceinversionz.

An object of the invention'is to invert the-impedance: of an impedancebranch; Further objects are to decreasethe size and cost,.and'im'- prove thetransmission characteristics, of wave transmission networks such as filters;

In accordance with the invention, a reactive impedance-branch isflarrangediwith a transistor and other component elements tov form a twoterminal network which has theproperty of effectively inverting the impedance of the'branc'h. The transistor is' -of the type having a basana collector, and an emitter; The branch to. be in.- verted ordinarily comprises an inductor and a resistor in parallel, and may include-one or more additional reactive parallel branches. Oneend of the branch is connected. toone of the. network terminals, and the other end.is:connected.through a source of direct voltage and a second resistor; which-may be adjustable; to the collector of the transistor. A third resistor is connectedrbetwe'en the base and the other network terminal. A feed; back is provided between thei'emitter-r and? a tap.- ping point on the inductor, the two? portions of which may be. inductively coupled to form an autotransformer. In some applications, it may be desirable to include a blocking capacitor in series with one of the network terminals. By making use of such an impedance inversiom an efiective capacitive or inductive reactance whichis too large or too small to be realized economically ma be obtained-from an inductor or a'capacitor-of ordinary size; Also, the equivalent-50f" a'large; high-Q inductor may be provided by usin'g a capacitor of only moderate size. In accordance with afurtherembodiment-of the invention, reactive impedances of this type are used in the branches of wave transmission networksito re duce the. size and cost and to improvethe transmission characteristics. As examples; band pass and band-elimination wave filters of the ladder type aredisclosed.

The nature of the invention and its various objects, features, and advantages will appear more fullyin the following detailed description of preferred embodiments illustrated in the accompany-- ing drawing; of which A g I Fig. 1 is a schematic circuit 0f a two-terminal network in accordance with'the' inventi'orrfor providing animpedanceinversion; v

Figs. 2 and 8 are schematic "circuits'-'-of-imped} ancebranches which may constitute tHe imped ance-"Z shown in Fig: 1; w r

Figs. 31 7; and 9 showschematically equivalent 2 impedance branches: obtainable with the network of F-ige l Figs. 4;15;.and*6'show, respectively; typical voltage, resistance, and reactance characteristics obtainab'le with the network of Fig. 1 when the impedance? Z is r a: capacitor; and

Figs 10 -an'd ll-are schematic circuits", respec tivelyi. or a: band=elimination and a; band-pass wave"filterembodyingthe invention.

The" embodiment of the impedance-inverting network in accordance'with the invention shown schematically in-Fig; 1 comprises a pair'of terminals Ii -and l5 between'which are connected a" transistor It; a source of direct voltage H, a capacitor CB; a general impedance Z; an inductor L, and:three resistorsR; Raand'RB; The transistor lfi comp'rises abase, a'colle'ctor, and-an emitter conn cted, respectivelwtotheterminals I9, 20'; and 2i. The transistor may beeither of the point-contact type or the-junction type, but the latter is: preferredbecause; in general, it provides a-more constantvalue of negative re'sistance for given applied potentials. Transistors of the-junc tion type-are"describeddn detail; for example, ina paper by: William Shockley-entitled,r-The theory ofp-njunctions in semiconductors and p-n junction-- transistors published in the" Bell System Technicalflournal; vol; XXVII-I;:pages 4'35 110489; July.1949,..ahd' thosebf:the point contact type in United States-Patent 2 ,524;035,zto=John Bardeen and-Walter H: Brattain', issued october 3;;1950: In Fig. 1, thesymbol used forthe' transistor Iii indicates thatit is of thejunction type, inasmuch as thel arrowhead 2 2- asso'ciate'd' with the eniitter points toward the terminal 2 If In *the symbol f or a p'oirit cont'act transistory-this" arrowhead is reversed.

Asshown'inF ig; 1, the resistor RB is connectedb'etweezi -the transistorbase-terminal I-9 and tl'ie network terminal 1 I42 The elements L,- R," andFZ are connected l in parallel between the network terminal 1 l5 and an I inner terminal- 241 vxrhiizh connected th the -collector terminal 20 through thesei'ies combination of' tl-ie vmta'gesource: ll and tlie resistor Rm The resistor- HA is prefr abl ymade "adjustable; as indicated by the arrow; to permit *adj ustm'e-n't of the effective" resistance of the 3 network, as 1 explained more fully below; In a I typicalcase; the value of Ra-may'ra'nge' be tween ze ro and '5,000 'ohm's and-the source li may be of-the' order of 2'2-volts'r A feedba'ck pathds provided by? connecting: the emitter' terminal E N to a tappingpoint.- 21, .preferablyfthe: midpoint, on the inductor=L. The portionssof th' inductor L on either side of the point 21 are preferably closely coupled inductively, thus constituting an autotransformer. In some applications, it is desirable to provide a blocking capacitor in series with one of the network terminals to prevent the establishment of an external direct-current path between the terminals I9 and of the transistor. As shown, the capacitor CB is included between the terminals I4 and I9 for this purpose. It should be large enough that its reactance will be sufficiently small to permit free passage of the alternating currents involved. A typical value for CB is a half microfarad.

The impedance branch Z may have any of a great variety of configurations. It may, for example be simply a capacitor C, as shown in Fig. 2. In this case, the equivalent circuit of the network of Fig. 1, as seen at the terminals I4 and I5, will be as shown schematically in Fig. 3, comprising a resistor R1 shunted by an arm comprising the series combination of a capacitor C1 and an inductor L1. The relationship between these elements and those appearing in Fig. 1 will be set forth below.

Figs. 4, 5, and 6 show, respectively, typical voltage, resistance, and reactance characteristics, plotted against frequency, obtainable with the network of Fig. 1 when the branch Z is a capacitor C having a value of one-thousandth microfarad, L has an inductance of one henry, CB has a capacitance of a half microfarad, and R and RB each have a resistance of 100,000 ohms. Fig. 4 gives the voltage in millivolts across the terminals I4 and I5 when a substantially constant current is supplied to the network. The voltage is, therefore, approximately proportional to the impedance of the network. It is seen that the characteristic dips sharply to a low value at the frequency fR, indicating that the impedance is series resonant at this frequency. The fact that the impedance is series resonant is confirmed by the resistance characteristics shown in Fig. 5, which have minimum values at IR, and the reactance characteristic shown in Fig. 6, which passes through zero with a steep positive slope at In. In Fig. 5, the upper resistance curve 25, which falls just to zero at in, is obtained with a fixed value of RB and a certain critical setting of the adjustable resistor RA. If the value of RA is increased, the curve is raised, and if it is decreased, the curve is lowered, without materially altering its shape. The lower curve 26 shows that the resistance of the network can be made negative throughout the frequency range of interest. The curve 26 may, for example, represent the resistive component of the impedance between the terminals I4 and I5 when RB is zero. The curve is obtained when BB is made equal in magnitude to the maximum negative value RM of the curve 26. If a portion of the curve is negative, the network becomes a source of energy, derived from the battery H, which may be used to compensate undesired energy dissipation in other impedance branches associated therewith. Examples are the filter circuits shown in Figs. 10 and 11, described below.

There will now be presented a suggested procedure for designing the network of Fig. 1 to have the equivalent circuit shown in Fig. 3. It will be assumed that the desired values of C1, L1, and R1 are known. In Fig. 1, it is assumed that the capacitance of CB is infinite and that the impedance branch Z is a capacitance C. The value of R13 is known at once, because RB=R1 .(1)

4 The value of R is selected in accordance with the best judgment of the designer, keeping in mind that, as R. increases, L tends to increase and C tends to decrease, and vice versa. The design formulas for C and L may be simplified by first finding the value of a fictitious resistance R? which depends upon R and the difference between the collector resistance To and mutual resistance Tm of the transistor I6, and is given by 4(r,,r,,,)R c"' m)+ Now, 0 and L are found from the formulas C=L1/R1RF (3) and L=R1RFC1 (4) The only element yet to be determined is RA. The proper setting for RA may be found by applying to the network a substantially constant current of the frequency in at which L1 and C1 are resonant, observing the voltage across the terminals I4 and I5 by means of an oscilloscope or vacuum-tube voltmeter, and adjusting RA for a voltage minimum of the type shown in Fig. 4.

The derivation of the above design formulas is too lengthy and too involved to be presented herein but it is based on the assumptions that the tapping point 24 of the autotransformer L is at the electrical midpoint and that the two halves of the winding have perfect inductive coupling, and the further assumption that the resistance RA and the base resistance and the emitter resistance of the transistor I6 are each small enough, when compared with other resistances such as the collector resistance Tc or the mutual resistance I'm, to be neglected. The actual performance of networks designed in accordance with the formulas shows that these assumptions are reasonable.

As an example of the application of the formulas, a network as shown in Fig. 1 in which GB is infinite and Z is constituted by C has been designed to have the equivalent circuit shown in Fig. 3, with the following assumed values:

C1=9.6 micromicrofarads (5) L1=91 henries (6) R1=100,000 ohms (7) From Equation 1, RB is 100,000 ohms. The value of R is selected as 100,000 ohms. Assuming that the difference between Tc and Tm is 325,000 ohms, a value readily attainable in a junction-type transistor, RF is found from Equation 2 to be Using Equations 3 and 4,

c=91 (100,000) (92,800) =0.0098 microfarad (9) and L=(100,000) (92,800) (9.6) (10- =0.089 henry czc'ro ees thousand and the ratio of L1 to L is the same. Furthermore, it is evident from Equations 2, 3, and 4 that this ratio may be changed within wide limit's'by choosing a difl erent value fonR" or-by selecting a transistor in" which the difference between To and Tm has some other value than that assumed.

As already suggested; it is not necessary that theimpedance b'ranch" Zin Fig; I be constituted by a capacitor: The bra'nch may-beomitted entirely, which casethe" equivalent circuit of the network will be as shown schematically in Fig. 7, comprising a capacitor C2 shunted by a resistor Re:

As another exam le the branch 2- may be'constituted by a capacitor C3 in series with an inductorlh, as shown schematically 8. Fig. 9 shows the, equivalent circuit of the network, com-prising aresistorRashunted by'an arm made up of-a capacitor C5 in se'rieswi'th the parallel combination of aca-pa'citor-C i andaninductor As a further extension of the invention, one or more networks of the type shown in Fig. 1 may-- beincorporated in the impedance branches of a wave transmission networkto reduce its size and cost and improve the transmission characteristic. As an example, Fig.. 10. shows a band-elimination wave filter section of the unbalanced ladd'er type comprising two parallelresonant series branches 28 and 29 and an interposed shunt branch NI connected between a pair of. input terminals 30, 3I and: a pair of output terminals32:, 33. The networksN-l is of the type showniin Fig. 1 between the terminals M andv IS, with the branch Z constitutedbyacapacitance .C. llhe equivalent circuit of. NI. will, therefore, be of the type shown in Fig. 3. If the shunting resistor R1 is chosen sufficiently large, the reactance of NI, as shown in Fig. 6, will simulate quite closely, over the frequency range of interest, the characteristic required for the shunt branch of the filter. Over this range, the reactance will, in fact, be essentially that of a capacitor C1 and an inductor L1 in series. For a certain critical setting of the resistor RA, the resistive characteristic of NI will be as shown by the curve 25 of Fig. 5, just touching zero at the resonant frequency fa. In this case, N I will act as a very high-Q, series-resonant circuit, but will supply no external energy. However, if RA is reduced in value, the resistance may be made negative over part or all of the frequency range of interest, as shown by the curve 26 of Fig. 5, which means that N1 is capable of furnishing external energy. The resistance RA may be set at a value such that the energy drawn from the network NI is of the right amount to compensate the undesired energy dissipation in the series branches 28 and 29, thus further reducing and flattening the loss of the filter in the transmission band and sharpening the cut-offs.

As another example, Fig. 11 shows a band-pass filter section of the ladder type comprising two series-connected networks N2 and N3, which may be similar to NI described above, and an interposed parallel-resonant shunt branch 34. Here, again, the networks N2 and N3 may be designed and adjusted to provide series-resonant impedances which are, in efiect, substantially dissipationless. Also, if desired, the resistor RA may be so set that the proper amount of negative resistance is furnished by N2, N3, or both, to compensate the energy dissipation in the shunt branch 34 and thus greatly improve the transmission characteristic of the filter.

Itis tebe understood that thesahova'descrlbcd arrangements are illustrative of the application of" the principles of the inventiom Numerous other arrangementsmay: be! devisedi by: those skilled in" the art without. departing: from"; the spirit and scope of the. inventiona What" is claimed is:

1. A network comprising: two; terminals; a transistor having axbasa aicollectonand aniemititer, a resistor connected: betweem one of said terminals: and said base, anzel'ectrical. path be.- tween said: collector andithe othen ofrsaiditemnianals, said path includingra so'urceioi voltagein series with the:parall'elicombinationzona second resistor and an inductor, andlai feedback path between saidemitter andatapping poiniionzsaid inductor.

2. A network in accordancawith claimliwhich includes-athird resistor conn'e'ct'edfin series. with said source.

3'. A network in: accordance with: claim: 2 in which said third" resistor: is". adjustable..

4. Av network in accordance: with. claim: 1;. in which the portions ofsaid inductcr 'on either-:side of said tapping point L are inductively coupledt 5a network in accordance: with claim;1: in which said tapping pointiisapproximatelyr the electrical midpoint of said inductor:

6. A network in: accordance with claim; 12' in which said: parallel combination. includes: am ad;- ditional parallel impedance-branch;

7. A network inuaccordanc'e" with. claim. 6-: in which said additionalbranch isreactivei.

8. A network in accordance with which said additional branch comprises a capac:

itor.

9. A network in. accordance with claim 6 in which said additional branch comprises a capacitor and a second inductor.

10. A network in .accordance with claim Grin which said additional branch comprises a capacitor and a second inductor connected in series.

11. A network in accordance with claim 1 in which said transistor is of the junction type.

12. A network in accordance with claim 1 which includes a blocking capacitor connected in series with one of said terminals.

13. A network in accordance with claim 1 in which said transistor has a base resistance and an emitter resistance each of which is small compared to either the collector resistance or the mutual resistance of said transistor.

14. A network comprising two terminals, a transistor having a base, a collector, and an emitter, a resistor connected between one of said terminals and said base, the parallel combination of a second resistor, a capacitor, and an inductor, connected at one end to the other of said terminals, a source of voltage and a third resistor connected in series between the other end of said parallel combination and said collector, and a feedback path between said emitter and a tapping point on said inductor.

15. A network in accordance with claim 14 in which said third resistor is adjustable.

16. A network in accordance with claim 14 in which the resistance of said third resistor is so chosen that the resistance of the network is substantially zero at one frequency only.

17. A network in accordance with claim 14 in which the resistance of said third resistor is so chosen that the resistance of the network is negative over a range of frequencies.

18. A network in accordance with claim 14 in which said transistor is of the junction type.

19. A network in accordance with claim 14 in which the portions of said inductor on either side of said tapping point are inductively coupled.

20. A network in accordance with claim 14 in which said tapping point is approximately the electrical midpoint of said inductor.

21. A network in accordance with claim 14 which includes a blocking capacitor connected in series with one of said terminals.

22. A network in accordance with claim 14 in which said transistor has a base resistance and an emitter resistance each of which is small compared to either the collector resistance or the mutual resistance of said transistor.

23. A network in accordance with claim 22 in which the resistance of said third resistor is small compared to either said collector resistance or said mutual resistance.

24. A network the equivalent circuit of which may be represented by a resistance R1 shunted by the series combination of capacitance C1 and an inductance L1, said network comprising a transistor having a base, a collector, and an emitter, a resistance RB connected between one of said terminals and said base, the parallel combination of a resistance R, a capacitance C, and an inductance Lconnected at one end to the other of said terminals, a resistance RA and a source of voltage connected in series between the other end of said parallel combination and said collector, and a feedback path between said emitter and approximately the midpoint of said inductance, RB, C, and L having approximately the following values:

and To and Tm are, respectively, the collector resistance and the mutual resistance of said transistor. v

25. A network in accordance with claim 24 in which R. has a value so chosen that the resistance of the network is substantialy zero at the resonant frequency of C1 and L1.

26. A network in accordance with claim 24 in which RA has a value so chosen that the network has a negative resistance. I

27. A network in accordance with claim 24 in which the two halves of said inductance are inductively coupled.

28. A network in accordance with claim 24 in which said transistor is of the junction type.

29. A network in accordance with claim 24 which includes a blocking capacitor connected in series with one of said terminals.

30. A network in accordance with claim 24 in which RA and the base resistance and the emitter resistance of said transistor are each small-compared to either To or m.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 1,725,154 Marsteller Aug. 20, 1929 1,772,506 Affel Aug. 12, 1930 2,505,266 Villem Apr. 25, 1950 2,544,211 Barton Mar. 6,1951

I 2,556,286 Meacham June 12, 1951 2,570,939 Goodrich Oct. 9, 1951 

